text: By Taylor series expansion, the potential energy, , of any molecule can be expressed as:
  :    (eq. 1)
  where  is a column vector of arbitrary and fully determined displacement coordinates, and  and  are the corresponding gradient (first derivative of ) and Hessian (second derivative of ), respectively. The point of interest is the stationary point on a potential energy surface (PES), so  is treated as zero, and by considering the relative energy,  as well becomes zero. By assuming harmonic potential and regarding the third derivative term and forth as negligible, the potential energy formula then simply becomes:
  :    (eq. 2)
  Transitioning from cartesian coordinates  to internal coordinates , which are more commonly used for the description of molecular geometries, gives rise to equation 3:
  :    (eq. 3)
  where  is the corresponding Hessian for internal coordinates (commonly referred to as force constants), and it is in principle determined by the frequencies of a sufficient set of isotopic molecules. Since the Hessian  is the second derivative of the energy with respect to displacements and that is the same as the first derivative of the force, evaluation of this property as shown in equation 4 is often used to describe chemical bonds.
  :    (eq. 4)
  Nevertheless, there are several issues with this method as explained by Grunenberg, including the dependence of force constants on the choice of internal coordinates and the presence of the redundant Hessian which has no physical meaning and consequently engenders ill-defined description of bond strength.